Merge pull request #331 from Selbl/cpp-problem-6

Problem 6 - C++ Solution

Author: moe18

Problems/6_calculate_eigenvalues/solution.cpp

@@ -0,0 +1,68 @@
+#include <iostream>
+#include <vector>
+#include <cmath> 
+#include <cassert> 
+
+using namespace std;
+
+vector<double> calculate_eigenvalues(const vector<vector<double> >& matrix)
+{
+    // Extract elements
+    double a = matrix[0][0];
+    double b = matrix[0][1];
+    double c = matrix[1][0];
+    double d = matrix[1][1];
+
+    // Get trace and determinant
+    double trace = a + d;
+    double determinant = a * d - b * c;
+    double discriminant = trace * trace - 4.0 * determinant;
+
+    // Solve for eigenvalues
+    double lambda1 = (trace + sqrt(discriminant)) / 2.0;
+    double lambda2 = (trace - sqrt(discriminant)) / 2.0;
+
+    // Return as vector
+    vector<double> eigenvalues(2);
+    eigenvalues[0] = lambda1;
+    eigenvalues[1] = lambda2;
+    return eigenvalues;
+}
+
+
+void test_calculate_eigenvalues()
+{
+    // Test Case 1
+    {
+
+        vector<vector<double> > matrix(2, vector<double>(2));
+        matrix[0][0] = 2.0;  matrix[0][1] = 1.0;
+        matrix[1][0] = 1.0;  matrix[1][1] = 2.0;
+
+        vector<double> result = calculate_eigenvalues(matrix);
+        assert(result.size() == 2);
+
+        assert(result[0] == 3.0);
+        assert(result[1] == 1.0);
+    }
+
+    // Test Case 2
+    {
+
+        vector<vector<double> > matrix(2, vector<double>(2));
+        matrix[0][0] = 4.0;   matrix[0][1] = -2.0;
+        matrix[1][0] = 1.0;   matrix[1][1] = 1.0;
+
+        vector<double> result = calculate_eigenvalues(matrix);
+        assert(result.size() == 2);
+
+        assert(result[0] == 3.0);
+        assert(result[1] == 2.0);
+    }
+}
+
+int main()
+{
+    test_calculate_eigenvalues();
+    return 0;
+}